Particulate systems in practical applications such as biomass combustion, blood cellular systems and granular particles in fluidized beds, have often been computationally represented using spherical surfaces, even though the majority of particles in archetypal fluid-solid systems are non-spherical. While spherical particles are more cost-effective to simulate, notable deficiencies of these implementations are their substantial inaccuracies in predicting the dynamics of particle mixtures. Alternatively, modeling dense fluid-particulate systems using non-spherical particles involves increased complexity, with computational cost manifesting as the biggest bottleneck. However, with recent advancements in computer hardware, simulations of three-dimensional particulate systems using irregular shaped particles have garnered significant interest. In this research, a novel Discrete Element Method (DEM) model that incorporates geometry definition, collision detection, and post-collision kinematics has been developed to accurately simulate non-spherical particulate systems. Superellipsoids, which account for 80% of particles commonly found in nature, are used to represent non-spherical shapes. Collisions between these particles are processed using a distance function computation carried out with respect to their surfaces. An event - driven model and a time-driven model have been employed in the current framework to resolve collisions. The collision model's influence on non–spherical particle dynamics is verified by observing the conservation of momentum and total kinetic energy. Furthermore, the non-spherical DEM model is coupled with an in-house fluid flow solver (GenIDLEST). The combined CFD-DEM model's results are validated by comparing to experimental measurements in a fluidized bed. The parallel scalability of the non-spherical DEM model is evaluated in terms of its efficiency and speedup. Major factors affecting wall clock time of simulations are analyzed and an estimate of the model's dependency on these factors is documented. The developed framework allows for a wide range of particle geometries to be simulated in GenIDLEST. / Master of Science / CFD – DEM (Discrete Element Method) is a technique of coupling fluid flow solvers with granular solid particles. CFD – DEM simulations are beneficial in recreating pragmatic applications such as blood cellular flows, fluidized beds and pharmaceutics. Up until recently, particles in these flows have been modeled as spheres as the generation of particle geometry and collision detection algorithms are straightforward. However, in real – life occurrences, most particles are irregular in shape, and approximating them as spheres in computational works leads to a substantial loss of accuracy. On the other hand, non – spherical particles are more complex to generate. When these particles are in motion, they collide and exhibit complex trajectories. Majority of the wall clock time is spent in resolving collisions between these non – spherical particles. Hence, generic algorithms to detect and resolve collisions have to be incorporated. This primary focus of this research work is to develop collision detection and resolution algorithms for non – spherical particles. Collisions are detected using inherent geometrical properties of the class of particles used. Two popular models (event-driven and time-driven) are implemented and utilized to update the trajectories of particles. These models are coupled with an in – house fluid solver (GenIDLEST) and the functioning of the DEM model is validated with experimental results from previous research works. Also, since the computational effort required is higher in the case of non – spherical particulate simulations, an estimate of the scalability of the problem and factors influencing time to simulations are presented.

[EN] The neutron diffusion equation is an approximation of the neutron transport equation that describes the neutron population in a nuclear reactor core. In particular, we will consider here VVER-type reactors which use the neutron diffusion equation discretized on hexagonal meshes. Most of the simulation codes of a nuclear power reactor use the multigroup neutron diffusion equation to describe the neutron distribution inside the reactor core.To study the stationary state of a reactor, the reactor criticality is forced in artificial way leading to a generalized differential eigenvalue problem, known as the Lambda modes equation, which is solved to obtain the dominant eigenvalues of the reactor and their corresponding eigenfunctions. To discretize this model a finite element method with h-p adaptivity is used. This method allows to use heterogeneous meshes, and allows different refinements such as the use of h-adaptive meshes, reducing the size of specific cells, and p-refinement, increasing the polynomial degree of the basic functions used in the expansions of the solution in the different cells. Once the solution for the steady state neutron distribution is obtained, it is used as initial condition for the time integration of the neutron diffusion equation. To simulate the behaviour of a nuclear power reactor it is necessary to be able to integrate the time-dependent neutron diffusion equation inside the reactor core. The spatial discretization of this equation is done using a finite element method that permits h-p refinements for different geometries. Transients involving the movement of the control rod banks have the problem known as the rod-cusping effect. Previous studies have usually approached the problem using a fixed mesh scheme defining averaged material properties and many techniques exist for the treatment of the rod cusping problem. The present work proposes the use of a moving mesh scheme that uses spatial meshes that change with the movement of the control rods avoiding the necessity of using equivalent material cross sections for the partially inserted cells. The performance of the moving mesh scheme is tested studying different benchmark problems. For reactor calculations, the accuracy of a diffusion theory solution is limited for for complex fuel assemblies or fine mesh calculations. To improve these results a method that incorporates higher-order approximations for the angular dependence, as the simplified spherical harmonics (SPN ) method must be employed. In this work an h-p Finite Element Method (FEM) is used to obtain the dominant Lambda mode associated with a configuration of a reactor core using the SPN approximation. The performance of the SPN (N= 1, 3, 5) approximations has been tested for different reactor benchmarks. / [ES] La ecuación de la difusión neutrónica es una aproximación de la ecuación del transporte de neutrones que describe la población de neutrones en el núcleo de un reactor nuclear. En particular, consideraremos reactores de tipo VVER y para simular su comportamiento se utilizará la ecuación de la difusión neutrónica para cuya discretización se hace uso de mallas hexagonales. La mayoría de los códigos de simulación de reactores nucleares utilizan aproximación multigrupo de energía de la ecuación de la difusión neutrónica para describir la distribución de neutrones en el interior del núcleo del reactor. Para estudiar el estado estacionario del reactor, es posible forzar la criticidad del reactor de forma artificial modificando las secciones eficaces de forma que se obtiene un problema de valores propios diferencial, conocido como el problema de los Modos Lambda, que se resuelve para obtener los valores propios dominantes del reactor y sus correspondientes funciones propias. Para discretizar este modelo se ha hecho uso de un método de elementos finitos con adaptabilidad h-p. Este método permite el uso de mallas heterogéneas, y de diferentes refinamientos como el uso mallas h-adaptativas, reduciendo el tamaño de los distintos nodos, y el p-refinado, aumentando el grado del polinomio de las funciones básicas utilizado en los desarrollos de la solución en los diferentes nodos. Se ha desarrollado un código basado en un método de elementos finitos de alto orden para resolver el problema de los Modos Lambda en un reactor con geometría hexagonal y se han obtenido los Modos dominantes para distintos problemas de referencia. Una vez que se ha obtenido la solución para la distribución de neutrones en estado estacionario, ésta se utiliza como condición inicial para la integración de la ecuación de difusión neutrónica dependiente del tiempo. Para simular el comportamiento de un reactor nuclear para un determinado transitorio, es necesario ser capaz de integrar la ecuación de la difusión neutrónica dependiente del tiempo en el interior del núcleo del reactor. La discretización espacial de esta ecuación se hace usando un método de elementos finitos de alto orden que permite refinados de tipo h-p para distintas geometrías. Los transitorios que implican el movimiento de los bancos de las barras de control tienen el problema conocido como el efecto 'rod-cusping'. Estudios anteriores, por lo general, han abordado este problema utilizando una malla fija y definiendo propiedades promedio para los materiales correspondientes a las celdas donde se tiene la barra de control parcialmente insertada. En el presente trabajo se propone el uso de un esquema de malla móvil, de forma que en mallado espacial va cambiando con el movimiento de la barra de control, evitando la necesidad de utilizar secciones eficaces equivalentes para las celdas parcialmente insertadas. El funcionamiento de este esquema de malla móvil propuesto se estudia resolviendo distintos problemas tipo. La precisión obtenida mediante de la teoría de la difusión en los cálculos de reactores es limitada cuando se tienen elementos de combustible complejos o se pretenden realizar cálculos en malla fina. Para mejorar estos resultados, es necesario disponer de un método que incorpore aproximaciones de orden superior de la ecuación del transporte de neutrones. Una posibilidad es hacer uso de las ecuaciones PN simplificadas (SPN ). En este trabajo se utiliza un método de elementos finitos h-p para obtener los modos dominantes asociados con una configuración dada del núcleo de un reactor nuclear con geometría hexagonal usando la aproximación SPN . El funcionamiento de las aproximaciones SPN (N = 1, 3, 5) se ha estudiado para distintos problemas de referencia. / [CA] L'equació de la difusió neutrònica és una aproximació de l'equació del transport de neutrons que descriu la població de neutrons en el nucli de un reactor nuclear. En particular, considerarem reactors de tipus VVER i per a simular el seu comportament s'utilitzarà l'equació de la difusió neutrónica que es discretitza fent ús de malles hexagonals. La majoria dels codis de simulació de reactors nuclears utilitzen l'aproximació multigrup d'energia de l'equació de la difusió neutrónica per a descriure la distribució de neutrons a l'interior del nucli del reactor. Per a estudiar l'estat estacionari del reactor, és possible forçar la seua criticitat de forma artificial modificant les seccions eficaces de manera que s'obté un problema de valors propis diferencial, conegut com el problema dels Modes Lambda, que es resol per a obtenir els valors propis dominants del reactor i les seues corresponents funcions pròpies. Per a discretitzar aquest model s'ha fet ús d'un mètode d'elements finits amb adaptabilitat h-p. Aquest mètode permet l'ús de malles heterogènies, i de diferents refinaments com l'ús malles h-adaptatives, reduint la grandària dels diferents nodes, i el p-refinat, augmentant el grau del polinomi de les funcions bàsiques utilitzat en els desenvolupaments de la solució en els diferents nodes. S'ha desenvolupat un codi basat en un mètode d'elements finits d'alt ordre per a resoldre el problema dels Modes Lambda en un reactor amb geometria hexagonal i s'han obtingut els Modes dominants per a diferents problemes de referència. Una vegada que s'ha obtingut la solució per a la distribució de neutrons en estat estacionari, aquesta s'utilitza com a condició inicial per a la integració de l'equació de difusió neutrònica depenent del temps. Per a simular el comportament d'un reactor nuclear per a un determinat transitori, és necessari ser capaç d'integrar l'equació de la difusió neutrónica depenent del temps a l'interior del nucli del reactor. La discretitzación espacial d'aquesta equació es fa usant un mètode d'elements finits d'alt ordre que permet refinats de tipus h-p per a diferents geometries. Els transitoris que impliquen el moviment dels bancs de les barres de control tenen el problema conegut com l'efecte 'rod-cusping'. Estudis anteriors, en general, han abordat aquest problema utilitzant una malla fixa i definint propietats equivalents per als materials corresponents a les cel·les on es té la barra de control parcialment inserida. En el present treball es proposa l'ús d'un esquema de malla mòbil, de manera que en mallat espacial va canviant amb el moviment de la barra de control, evitant la necessitat d'utilitzar seccions eficaces equivalents per a les cel·les parcialment inserides. El funcionament de aquest esquema de malla mòbil s'estudia resolent diferents problemes tipus. La precisió obtinguda mitjançant de la teoria de la difusió en els càlculs de reactors és limitada quan es tenen elements de combustible complexos o es pretenen realitzar càlculs en malla fina. Per a millorar aquests resultats, és necessari disposar d'un mètode que incorpore aproximacions d'ordre superior de l'equació del transport de neutrons. Una possibilitat és fer ús de les equacions PN simplificades (SPN ). En aquest treball s'utilitza un mètode d'elements finits h- p per a obtenir els modes dominants associats amb una configuració donada del nucli de un reactor amb geometria hexagonal usant l'aproximació SPN . El funcionament de les aproximacions SPN (N = 1, 3, 5) s'ha estudiat per a diferents problemes de referència. / Fayez Moustafa Moawad, R. (2016). Approximation of The Neutron Diffusion Equation on Hexagonal Geometries Using a h-p finite element method [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/65353

One of the characteristics of the high speed ows over blunt bodies is the detached shock formed in front of the body. The distance of the shock from the stagnation point measured along the stagnation streamline is termed as the shock stand o distance or the shock detachment distance. It is one of the most basic parameters in such ows. The need to know the shock stand o distance arises due to the high temperatures faced in these cases. The biggest challenge faced in high enthalpy ows is the high amounts of heat transfer to the body. The position of the shock is relevant in knowing the temperatures that the body being subjected to such ows will have to face and thus building an efficient system to reduce the heat transfer. Despite being a basic parameter, there is no theoretical means to determine the shock stand o distance which is accepted universally. Deduction of this quantity depends more or less on experimental or computational means until a successful theoretical model for its predictions is developed. The experimental data available in open literature for spherical bodies in high speed ows mostly lies beyond the 2 km/s regime. Experiments were conducted to determine the shock stand o distance in the velocity range of 1-2 km/s. Three different hemispherical bodies of radii 25, 40 and 50 mm were taken as test models. Since the shock stand o distance is known to depend on the density ratio across the shock and hence gamma (ratio of specific heats), two different test gases, air and carbon dioxide were used for the experiments here. Five different test cases were studied with air as the test gas; Mach 5.56 with Reynolds number of 5.71 million/m and enthalpy of 1.08 MJ/kg, Mach 5.39 with Reynolds number of 3.04 million/m and enthalpy of 1.42 MJ/kg Mach 8.42 with Reynolds number of 1.72 million/m and enthalpy of 1.21 MJ/kg, Mach 11.8 with Reynolds number of 1.09 million/m and enthalpy of 2.03 MJ/kg and Mach 11.25 with Reynolds number of 0.90 million/m and enthalpy of 2.88 MJ/kg. For the experiments conducted with carbon dioxide as test gas, typical freestream conditions were: Mach 6.66 with Reynolds number of 1.46 million/m and enthalpy of 1.23 MJ/kg. The shock stand o distance was determined from the images that were obtained through schlieren photography, the ow visualization technique employed here. The results obtained were found to follow the same trend as the existing experimental data in the higher velocity range. The experimental data obtained was compared with two different theoretical models given by Lobb and Olivier and was found to match. Simulations were carried out in HiFUN, an in-house CFD package for Euler and laminar own conditions for Mach 8 own over 50 mm body with air as the test gas. The computational data was found to match well with the experimental and theoretical data

The well known synthesis problem of obtaining dimensions of a four-link mechanism such that a point on the coupler link traces a desired path has been extensively studied. There are two types of path generation–path specified by a finite number of precision points where the prescribed points must be exactly traced, and continuous path generation where the path is approximately traced by the coupler point. In various application, more than one or multiple paths are required to be traced by the coupler point and in such cases, adjustable four-link mechanisms where one of the dimension or parameters of the mechanism can be changed is a possible solution. This thesis deals with the synthesis of planar and spherical adjustable four-link crank-rocker type mechanisms for multiple continuous path generation. Approximate multiple path generation is typically solved as an optimization problem where the dimensions and parameters of the four-link mechanism are obtained such that the objective functions, typically in terms of an error between the desired and obtained path, is minimized. In this thesis, we present a two-stage optimization to obtain four-link mechanism dimensions such that the adjustable four-link mechanism can approximately trace multiple desired paths. In the first stage, the parameters in the driving side of the four-link mechanism is obtained and in the second stage, the parameters of the driven side are obtained. In case of adjustable planar four-link mechanism, a novel optimization objective function based on circle-fitting is used and for spherical adjustable mechanisms a novel plane-fitting based objective function is used. The use of these objective functions results in a lesser number of variables to be searched and thus the method presented in this work is more efficient than existing optimization based algorithms available in literature. Several examples are presented for synthesis of adjustable planar and spherical four-link mechanism for tracing multiple paths. In particular, a spherical mechanism which can generate an oval and an‘ 8’shaped path by one single adjustment is synthesized. This mechanism has been made using 3D printing and it is shown that the mechanism indeed traces the desired oval and ‘8’ shaped paths. This mechanism is being planned for use in a flapping wing micro air vehicle where the oval shaped path is known to make the vehicle to move forward while the ‘8’ shaped path results in a hovering motion.

For the transport of their spacecraft from the vehicle assembly building to the launch pads at Kennedy Space Centre, Florida, the National Aeronautics and Space Administration (NASA) is using two special crawler transporters since 1965. First developed for the Saturn V rocket the crawler transporters have been sufficient for all following generations of space ships so far. But for the new generation of Orionspacecraft which is under development now, a load capacity increase for the crawler transporter of plus 50% was necessary. For this task Hunger Hydraulik did develop new jacking, equalizing and levelling (JEL) cylinders with sufficient load capacity but also with some new features to improve the availability, reliability and safety of this system. After design approval and manufacture of the cylinders they have been tested in a special developed one-to-one scale dynamic test rig and after passing this the cylinders had to prove their performance in the crawler transporter itself. This article describes the general application and introduces the technical requirements of this project as well as the realized solution.

This dissertation attempts to understand how energy transfer in a molecular wire and a spherical organic assembly are affected by molecular structure. The molecular wire is a DNA-hybrid structure composed of a strand of thymine bases appended by a cyanine dye. Hydrogen bonded to each base is a naphthalene-derivative molecule. Using time-integrated photoluminescence and time-correlated single photon counting measurements, energy transfer from the naphthalene donors to the cyanine acceptors was confirmed, and its dependence on temperature and DNA-template length investigated. Donor-thymine bonding was disrupted at temperatures above about 25 degrees Celcius resulting in poor donor template decoration and low rates of energy transfer. Increasing numbers of donors attach to the scaffold, forming an orderly array, as the template length increases due to the stabilising effects of the donor-donor pi-stacking interactions. Conversely, modelled energy transfer rates fall as the scaffold length increases because of the longer donor-acceptor distances involved. Therefore, the energy transfer rate was greatest for a template built from 30 thymines. The spherical organic assemblies (nanoparticles) are formed by fast injection of a small volume of molecularly dissolved fluorene-derivative amphiphilic molecules into a polar solvent. The amphiphilic molecules contained either a naphthalene (donor) or a benzothiadiazole (acceptor) core. The donor-acceptor mixed nanoparticles resemble an amorphous polymer film and were modelled as such using the Foerster resonance energy transfer theory. The Foerster radii extracted from the measurements depends intricately on the donor-acceptor spectral overlap and distance. The latter effect was controlled by the stacking interactions between the molecules. Altering the morphology of the structural units is the key to optimising energy transfer in molecular structures. To achieve efficient organic molecule-based devices, the importance of this property needs to be fully appreciated and effectively exploited.

L'objet de ce travail est de prouver des théorèmes de géométrie hyperbolique en utilisant des méthodes développées par Euler, Schubert et Steiner en géométrie sphérique. On donne des analogues hyperboliques de certaines formules trigonométriques en utilisant la méthode des variations et une formule pour l'aire d'un triangle. Euler utilisa cette idée en géométrie sphérique.On résout ensuite le problème de Lexell en géométrie hyperbolique. Cette partie est basée sur un travail en collaboration avec Weixu Su. En utilisant l'analogue hyperbolique des identités de Cagnoli, on prouve deux résultats classiques en géométrie hyperbolique. Ensuite, on donne les solutions aux problèmes de Schubert (en collaboration avec Vincent Alberge) et de Steiner. En suivant les idées de Norbert A'Campo, on donne l'ébauche de la preuve de la formule de Schlafli en utilisant la géométrie intégrale. Cette recherche peut être généralisée partiellement au cas de la dimension 3. / Our aim is to prove sorne theorems in hyperbolic geometry based on the methods of Euler, Schubert and Steiner in spherical geometry. We give the hyperbolic analogues of sorne trigonometrie formulae by method of variations and an a rea formula in terms of sides of triangles, both due to Euler in spherical case. We solve Lexell's problem. This is a joint work with Weixu Su. We give a shorter formula than Euler's a rea formula. Using hyperbolic analogues of Cagnoli's identities, we prove two classical results in hyperbolic geometry. Further, we give solutions of Schubert's and Steiner's problems. The study of Schubert's problem is a joint work with Vincent Alberge. Finally, following ideas of Norbert A' Campo, we give the sketch of the proof of Schlafli formula using integral geometry. The mentioned theorems can be generalized to the case of dimension 3 partially by means of the techniques used developed in this the sis.

A análise de dados composicionais está sendo amplamente utilizada nas diversas áreas do conhecimento como por exemplo na análise de sedimentos rochosos, na comparação de diferentes células e até na análise criminalística na comparação de evidências de crimes. Durante a história da análise deste tipo de dados existiram muitos tipos de ajustes utilizados para contornar o problema da soma constante das variáveis e ainda hoje não temos um consenso de qual a melhor solução a ser utilizada. Neste trabalho, temos como objetivo a enunciação das 7 transformações que mais foram utilizadas ao longo do tempo e suas vantagens e desvantagens. A análise de componentes principais foi escolhida para o comparativo destas transformações. Fizemos a aplicação destas transformações em três bancos de dados reais com características diferentes entre si, comparamos os resultados e analisamos qual das transformações apresentou o melhor desempenho em cada base de dados. Os critérios de comparação foram o percentual da variância explicada, as variáveis que foram mais importantes para a primeira componente principal, cargas das variáveis nas componentes principais mais importantes assim como suas correlações com as variáveis. Também, simulamos quatro estruturas de bases de dados composicionais para avaliar o desempenho das transformações. Para essas comparações e simulações, foram desenvolvidas algumas funções, utilizando o \\textit estatístico R, que visam facilitar a comparação entre as sete transformações, assim auxiliando na escolha de qual das transformações melhor se adapta aos dados. Pelos resultados obtidos notamos que: nas bases de dados reais, os resultados das explicações da variância das transformações são similares e as transformações Ref e Alr mostram melhores desempenhos que as demais; nas quatro estruturas simuladas as transformações Ref e Alr também possuem os melhores resultados na explicação da variância e a interpretação de suas componentes principais são parecidas, assim como as transformações Trad, Log e Clr. Com isso notamos que independentemente da aplicação do logaritmo nas transformações Alr e Log elas apresentaram resultados muitos similares às transformações Ref e Trad, respectivamente, tanto na explicação da variância como na interpretação das componentes principais. / The compositional data analysis is being widely used in several areas of knowledge such as the analysis of rocky sediments, to compare different biological cells and even in forensic analysis to compare crimes evidences. During the history of the analysis of such data, to circumvent the problem of variable\'s constant sum were used many types of adjustments. Until now, we do not have a consensus in which is the best solution to be used in this cases. In this paper, we aim to enunciate seven transformations that most were used over time and their advantages and disadvantages. The principal component analysis was chosen for the comparison of these transformations. We applied this transformations in three real databases with different characteristics, we hope to compare the results and analyze which transformation have the best performance in each database. The comparison criteria were the percentage of explained variance, the variables that were most important to the first principal component,variable\'s loads in the most important principal components as well their correlation with the variables. We also simulated four compositional data bases structures to evaluate the performance of the transformations. For these comparisons and simulations were developed some functions, using the statistical software R, to facilitate comparison between the seven transformations, thus assisting in choosing which of the best transformation fits to the data. From the results we note that: for the real databases, the results of the variance explanation of all transformations are similar, thus Ref and Alr transformations show better performances than the others; in the four simulated structures the Ref and Alr transformations also have the best results in the variance explanation and interpretation of its main components are similar, as well as the transformations Trad, Log and Clr. Thus we note that independently of applying logarithm in and Log and Alr transformations they present very similar results as Ref and Trad transformations, respectively, both in variance explanation and in the interpretation of the principal components.

A análise de dados composicionais está sendo amplamente utilizada nas diversas áreas do conhecimento como por exemplo na análise de sedimentos rochosos, na comparação de diferentes células e até na análise criminalística na comparação de evidências de crimes. Durante a história da análise deste tipo de dados existiram muitos tipos de ajustes utilizados para contornar o problema da soma constante das variáveis e ainda hoje não temos um consenso de qual a melhor solução a ser utilizada. Neste trabalho, temos como objetivo a enunciação das 7 transformações que mais foram utilizadas ao longo do tempo e suas vantagens e desvantagens. A análise de componentes principais foi escolhida para o comparativo destas transformações. Fizemos a aplicação destas transformações em três bancos de dados reais com características diferentes entre si, comparamos os resultados e analisamos qual das transformações apresentou o melhor desempenho em cada base de dados. Os critérios de comparação foram o percentual da variância explicada, as variáveis que foram mais importantes para a primeira componente principal, cargas das variáveis nas componentes principais mais importantes assim como suas correlações com as variáveis. Também, simulamos quatro estruturas de bases de dados composicionais para avaliar o desempenho das transformações. Para essas comparações e simulações, foram desenvolvidas algumas funções, utilizando o \\textit estatístico R, que visam facilitar a comparação entre as sete transformações, assim auxiliando na escolha de qual das transformações melhor se adapta aos dados. Pelos resultados obtidos notamos que: nas bases de dados reais, os resultados das explicações da variância das transformações são similares e as transformações Ref e Alr mostram melhores desempenhos que as demais; nas quatro estruturas simuladas as transformações Ref e Alr também possuem os melhores resultados na explicação da variância e a interpretação de suas componentes principais são parecidas, assim como as transformações Trad, Log e Clr. Com isso notamos que independentemente da aplicação do logaritmo nas transformações Alr e Log elas apresentaram resultados muitos similares às transformações Ref e Trad, respectivamente, tanto na explicação da variância como na interpretação das componentes principais. / The compositional data analysis is being widely used in several areas of knowledge such as the analysis of rocky sediments, to compare different biological cells and even in forensic analysis to compare crimes evidences. During the history of the analysis of such data, to circumvent the problem of variable\'s constant sum were used many types of adjustments. Until now, we do not have a consensus in which is the best solution to be used in this cases. In this paper, we aim to enunciate seven transformations that most were used over time and their advantages and disadvantages. The principal component analysis was chosen for the comparison of these transformations. We applied this transformations in three real databases with different characteristics, we hope to compare the results and analyze which transformation have the best performance in each database. The comparison criteria were the percentage of explained variance, the variables that were most important to the first principal component,variable\'s loads in the most important principal components as well their correlation with the variables. We also simulated four compositional data bases structures to evaluate the performance of the transformations. For these comparisons and simulations were developed some functions, using the statistical software R, to facilitate comparison between the seven transformations, thus assisting in choosing which of the best transformation fits to the data. From the results we note that: for the real databases, the results of the variance explanation of all transformations are similar, thus Ref and Alr transformations show better performances than the others; in the four simulated structures the Ref and Alr transformations also have the best results in the variance explanation and interpretation of its main components are similar, as well as the transformations Trad, Log and Clr. Thus we note that independently of applying logarithm in and Log and Alr transformations they present very similar results as Ref and Trad transformations, respectively, both in variance explanation and in the interpretation of the principal components.

Made available in DSpace on 2016-04-27T16:58:21Z (GMT). No. of bitstreams: 1 irene pataki.pdf: 2012677 bytes, checksum: 06b1249e92ce7aa730b0c645dcdc5ae1 (MD5) Previous issue date: 2003-11-28 / This work concerns the inservice education of mathematics teachers. One of its aims is to propose, to teachers, a teaching sequence, with activities that show the interdisciplinary relationship that exists between spherical geometry and geography, forming interconnections between these domains, at the same time as contextualising the content to be considered and motivating learning in a way that articulates the object of study with reality. Another aim is to provide to the teachers involved reflections about aspects related to the teaching of spherical geometry. Based on the Theory of Didactic Situation developed by G. BROUSSEAU (1986), the research methodology Didactic Engineering of M. ARTIGUE (1988) and the theory of Britt-Mari BARTH (1993) concerning teacher education, we elaborate a teaching sequence, composed of a motivating problem-situation along with eight other activities involving notions of spherical geometry. We investigate the question: How can a teaching sequence permit the appropriation of a new domain spherical geometry and encourage educators to re-elaborate their thinking? Our research hypotheses assume that geometrical knowledge allows different perspectives about our world, that the apprehension of content can lead to changes in our behaviour as teachers and that the use of interdisciplinarity and contextualisation will establish connections between different fields of knowledge. The analysis of the results points to a change in the attitudes and values of the teachers, which confirms our research hypothesis and emphasises the importance of the methodology adopted, leading us to believe that some aspects of the geometry studies were learnt and became institutionalised knowledge / Este trabalho dirige-se à formação continuada de professores de Matemática. Um dos seus objetivos é propor, aos professores, uma seqüência didática, com atividades, que mostre a relação interdisciplinar existente entre a Geometria esférica e a Geografia, formando interconexões entre esses domínios, ao mesmo tempo em que contextualiza os conteúdos a serem considerados e possibilita uma aprendizagem motivadora, que articule o objeto de estudo com a realidade. Outro objetivo é proporcionar aos professores envolvidos reflexões e questionamentos sobre alguns aspectos do ensino da Geometria esférica. Fundamentados na Teoria das Situações Didáticas desenvolvida por G. BROUSSEAU (1986), na Metodologia de Pesquisa denominada Engenharia Didática de M. ARTIGUE (1988) e na Teoria de Britt-Mari BARTH (1993) concernente à Formação de Professores, elaboramos uma seqüência didática, a partir de uma situação-problema motivadora e mais oito atividades, abordando noções de Geometria esférica. Investigamos a questão: Como uma seqüência de ensino pode possibilitar a apropriação de um novo domínio a Geometria esférica e levar o educador a reelaborar seu pensar? Nossas hipóteses de pesquisa pressupõem que o conhecimento geométrico nos permite ter olhares diferentes do nosso mundo, que a apreensão dos conteúdos poderá nos conduzir a mudanças no comportamento como docente e que o uso da interdisciplinaridade e da contextualização estabelecerá conexões com outros campos do conhecimento. A análise dos resultados obtidos aponta uma mudança de atitudes e valores, nos professores, que confirmam nossas hipóteses de pesquisa e enfatizam a importância da Metodologia adotada, levando-nos a crer que alguns aspectos da Geometria em estudo foram apreendidos e se tornaram saberes institucionalizados